解答 - 几何数列

要找到系列的通用形式，将第一项：$$a=160,000$$ 和公比：$$r=0.4096$$ 插入几何级数的公式：

$$a_1=160000$$

$$a_2=a_1·r^{n-1}=160000\cdot {0.4096}^{2-1}=160000\cdot {0.4096}^1=160000\cdot 0.4096=65536$$

$$a_3=a_1·r^{n-1}=160000\cdot {0.4096}^{3-1}=160000\cdot {0.4096}^2=160000\cdot 0.16777216=26843.5456$$

$$a_4=a_1·r^{n-1}=160000\cdot {0.4096}^{4-1}=160000\cdot {0.4096}^3=160000\cdot 0.06871947673600001=10995.116277760002$$

$$a_5=a_1·r^{n-1}=160000\cdot {0.4096}^{5-1}=160000\cdot {0.4096}^4=160000\cdot 0.028147497671065606=4503.599627370497$$

$$a_6=a_1·r^{n-1}=160000\cdot {0.4096}^{6-1}=160000\cdot {0.4096}^5=160000\cdot 0.011529215046068473=1844.6744073709556$$

$$a_7=a_1·r^{n-1}=160000\cdot {0.4096}^{7-1}=160000\cdot {0.4096}^6=160000\cdot 0.004722366482869647=755.5786372591434$$

$$a_8=a_1·r^{n-1}=160000\cdot {0.4096}^{8-1}=160000\cdot {0.4096}^7=160000\cdot 0.0019342813113834073=309.48500982134516$$

$$a_9=a_1·r^{n-1}=160000\cdot {0.4096}^{9-1}=160000\cdot {0.4096}^8=160000\cdot 0.0007922816251426436=126.76506002282298$$

$$a_{10}=a_1·r^{n-1}=160000\cdot {0.4096}^{10-1}=160000\cdot {0.4096}^9=160000\cdot 0.00032451855365842687=51.9229685853483$$